Hi, and Welcome to the Great American RoadTrip Forum.
You can easily do that in 10 days. Especially since you have another day up your sleeve. If you were only to average 35 mph - which is most unlikely - it would take around 9 hours on the road for 10 days. At just over 3000 miles, you would only need to cover about 300 miles per day. Breaking it down like that, you can see, it should be a trip with time to stop at all the hilights and not be rushed.
There are quite a few sites about this great road, of which I have only driven bits here and there. Brian Butko's books on this road are the best available, here's one to look at.
Lifey